1. Field of Invention
This invention relates to burst mode digital communication systems where data transmission is preceded by an alternating binary phase shift keying (BPSK) preamble for rapid acquisition of carrier and symbol synchronization. The preamble is sampled and the set of samples obtained are processed to provide carrier and symbol phase estimates.
2. Description of Related Art
One of the techniques used in burst mode digital communication systems is time division multiple access (TDMA). This technique allows multiple users to share a single communication channel. Each user is assigned a time slot in which to transmit data. The time slot is measured from a frame marker which repeats at a fixed period. The time slot can be variable in length and can be preassigned or assigned as needed on demand.
To control and configure a TDMA system, a time interval called a is frame is defined. A frame is divided into time slots, and a burst consists of an integer number of slots. Bursts typically consist of a preamble, a unique word and random symbol data (message portion).
A receiver uses the preamble to synchronize its processor with the time and frequency of the signal it is receiving. A preamble consists of a signal interval for carrier and symbol-timing recovery and a unique word for burst synchronization and other symbols.
In order to establish communications, carrier and symbol synchronization must take place. A digitally implemented BPSK demodulator, a portion of which is shown in FIG. 1, performs these functions. The basic functions of the different elements are as follows.
A sampling interpolator unit 1 calculates output sample components, X and Y, twice per symbol at the instants defined by the timing reference from the symbol synchronizer. In some implementations, the interpolator is removed and the analog-to-digital converter sampling times are defined by the timing reference.
A coherent demodulator unit 3 provides soft decision sample values to a decoder that follows.
A system timing unit 5 controls the timing of the carrier and symbol acquisition and synchronization functions.
A carrier and symbol acquisition unit 2 generates initial carrier and phase estimates that are input into a carrier synchronizer unit 4 and symbol synchronizer unit 6, respectively.
A carrier synchronization unit 4 generates a reference carrier with a phase closely matching that of the data signal. It provides the estimates of carrier frequency and phase which are necessary for coherent demodulation.
A symbol synchronizer unit 6 provides the timing reference required for sampling at the correct intervals so that bit decisions can be made on the data symbols. Further information on burst demodulators is contained in an article by S. A. Rhodes and S. I. Sayegh entitled, "Digital On-board Demodulator for Reception of an Up-link Group of TDMA/QPSK Channels," Proceedings of ICDSC8, Guadalupe, F.W.I., April 1989, which is incorporated herein by reference.
The present invention is related to the carrier and symbol acquisition functions.
TDMA system timing prior to signal acquisition is assumed to be available with an accuracy of a few symbol intervals. This timing is used to gate the acquisition and tracking modes for carrier and symbol synchronization.
Complex time domain samples, Z=X+jY, are used to represent the quadrature components of a received signal, after demodulation, with a carrier reference of approximately the correct frequency, but an arbitrary phase angle. Quadrature samples of the desired channel are input to a sample interpolator at a rate of approximately three complex samples per symbol. Another input to the sample interpolator feeds back the estimated symbol timing from the symbol synchronizer.
In-phase and quadrature samples of the BPSK preamble are sampled at the rate of N.sub.S complex (in-phase and quadrature) samples per symbol, where N.sub.S is typically (but not necessarily) equal to 2 samples per symbol.
Denoting the carrier phase by .theta..sub.R, and the clock phase by T.sub.R, and noting that the received filtered alternating preamble is sinusoidal, the following expressions may be written: EQU X.sub.n =cos(.theta..sub.R)*cos(.pi.R.sub.s nT+T.sub.R) EQU Y.sub.n =sin(.theta.R)*cos(.pi.R.sub.s nT+T.sub.R)
where X.sub.n is the in-phase sample, Y.sub.n is the quadrature sample, R.sub.s is the symbol rate, and T the sampling interval.
These samples are correlated with samples from a sine and a cosine waveform that have the same period as the alternating BPSK preamble, namely with sin(.pi.R.sub.s nT) and cos(.pi.R.sub.s nT).
Correlating the in-phase received samples with a sine and a cosine waveform produce odd and even in-phase sample correlations X.sub.o (odd) and X.sub.E (even), respectively, as shown below. Similarly, correlating the quadrature received samples with a sine and a cosine waveform produce odd and even quadrature sample correlations Y.sub.O (odd) and Y.sub.E (even), respectively, as shown below: EQU X.sub.o =-cos(.theta..sub.R)*sin(T.sub.R) EQU X.sub.E =cos(.theta..sub.R)*cos(T.sub.R) EQU Y.sub.o =-sin(.theta..sub.R)*sin(T.sub.R) EQU Y.sub.E =sin(.theta..sub.R)*cos(T.sub.R)
These correlations result in four correlations values X.sub.O, X.sub.E, Y.sub.O, and Y.sub.E. In the absence of a significant frequency offset, these four values are sufficient to derive the desired initial carrier and symbol phase estimates.
Two algorithms are readily available for processing the preamble samples. However, the first algorithm is overly sensitive to any amplitude slope that may be present over a non-equalized communication channel. The second algorithm is not sensitive to amplitude slope, however, it requires more hardware than the present invention to implement.
The purpose of the invention is to provide a method and apparatus for obtaining initial carrier and symbol phase estimates that can be easily implemented with a minimal amount of hardware. This is accomplished by deriving the maximum likelihood algorithms and mapping them into an easily implementable set of equations. The actual hardware implementation is described in the detailed description section.
All of algorithms discussed here (the existing two and the subject of the invention) use the four correlation values X.sub.O, X.sub.E, Y.sub.O, and Y.sub.E to derive the desired initial carrier and symbol phase estimates. The differences among the three algorithms lie in how the four values are processed.
Once obtained, these initial carrier and clock phase estimates initialize the synchronizers at the end of the preamble. These initialization values represent memory inherent in the accumulators for the phase-locked loops that are used in the tracking mode of synchronization.
In existing algorithm 1, the initial carrier phase estimate (THETAHAT) and initial symbol phase estimate (TAUHAT) are obtained as follows: ##EQU1##
The main problem with this algorithm is that in the presence of an amplitude slope over the communications channel, the estimates obtained by the algorithm may be grossly inaccurate. FIG. 2 illustrates this fact by showing how the estimated value of the angle (THETAHAT or TAUHAT) is significantly different from the actual value (.theta..sub.R or T.sub.R), if an amplitude slope of a few dBs is present on the link.
In existing algorithm 2, the initial carrier and symbol phase estimates are obtained by the following expressions: EQU ANUM=2((X.sub.o *Y.sub.o)+(X.sub.E *Y.sub.E)) EQU ADEN=(X.sub.E *X.sub.E)-(Y.sub.E *Y.sub.E)+(X.sub.O *X.sub.O)-(Y.sub.o *Y.sub.O) EQU THETAHAT=0.5arctan(ANUM/ADEN) EQU BNUM=-2((X.sub.O *X.sub.E)+(Y.sub.o *Y.sub.E)) EQU BDEN=(X.sub.E *X.sub.E)+(Y.sub.E *Y.sub.E)-(*X.sub.O *X.sub.O)-(Y.sub.O *Y.sub.O) EQU TAUHAT=0.5arctan(BNUM/BDEN)
Implementation of this algorithm results in more accurate estimates, however, it requires more hardware than algorithm 1, making it unattractive for applications requiring a compact implementation.